Foundation Physics

Lecture 2.4

26 Jan ‘10

Temperature and Heat

Temperature, Internal Energy and Heat

• What is temperature?

• What is heat?

• What is internal energy?

Temperature

Internal EnergyDoes a glass of water sitting on a table have any energy?

No apparent energy of the glass of water on a macroscopic scale.

Microscopic kinetic energy is part of internal energy.Molecular attractive forces are associated with potential energy.

Atoms, molecules, Phases of Matter

Matter (solid, liquid or gas) is made up of atoms and molecules or particles which are in continual motion.Total kinetic energy of the particles in a given body is directly proportional to the absolute temperature of the body. Kinetic energy of the gas molecules would become zero at absolute zero, and molecular motion would cease.Potential energy of the particles is due to electrostatic interactions of the electrons and the nuclei which exert forces on each other.Total internal energy of a body is the sum of potential energy and kinetic energy of the molecules in the body.

Phases (solid)

Solid

Solid: In a solid material, the attractive forces are strong enough that the molecules are packed closely in an orderly way. At the same time, there are also repulsive forces so that the molecules cannot penetrate into one another. Thus the molecules are held in more or less fixed positions. The molecules in a solid vibrate about their nearly fixed positions, usually in an array known as crystal lattice.

Phases (Liquid)

Liquid

Liquid: In a liquid, the molecules are moving more rapidly, or the forces between them are weaker, so that they are sufficiently free to roll over one another.

Phases (Gas)

Gas

Gas: In a gas, the forces are so weak, or the speeds so high, that the molecules do not even stay close together. They move rapidly every which way, filling any container and occasionally colliding with one another. For an ideal gas, the intermolecular forces are assumed to be negligible and thus, potential energy is zero.

Microscopic ExplanationWe look at the interaction potential of to neighbouring atoms

r0: Distance between two atoms at T0= 0K (minimal thermal motion of the atoms)

r1: Average position of the atom at T1>T0

r1>r0: due to the asymmetry of the potential

E

r0

r1

Ep

Thermometers and Temperature Scales

Objectives are to:

• define what a thermometer is• describe the physical principles on which the use of a thermometer is based• state the Zeroth Law of Thermodynamics, and discuss its physical implications with respect to thermometers• explain how a temperature scale is constructed• convert temperatures from one scale to another• obtain a feel for the range of temperature values in everyday life and throughout the Universe

Temperature and Heat

Temperature is the physical property which determines the direction of net flow of heat.Heat is the net energy that is transferred from one object to another due to temperature difference between the two objects in thermal contact.

Thermal equilibrium exists for two bodies which are in thermal contact with no net flow of heat between them.Zeroth Law of Thermodynamics states that if bodies A and B are separately in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other.

Scales of temperature

• The Thermodynamic Scale of Temperature (also known as Kelvin Scale) is totally independent of the properties of any particular substance and is therefore an absolute scale of temperature. The fixed points are the triple point of water (273.16 K or 0.01˚C) and absolute zero (0 K or –273.15˚C).

• The kelvin is the SI unit of temperature in the thermodynamic scale. One kelvin is thus defined to be 1/273.16 of the thermodynamic temperature of the triple point of water.

• The Celsius Scale is related to the Thermodynamic Scale by the equation t/oC = T/K – 273.15.

Zeroth Law of Thermodynamics

If bodies A and B are separately in thermal equilibrium with a third body, C, then A and B will be in thermal equilibrium

with each other if placed in thermal contact.

Temperature Scales

Conversion of temperature sclaes

[ ]

[ ]

15.273)()(

32)(59)(

32)(95)(

+°=

°+°=°

°−°=°

CTKT

CTFT

FTCT

Problem: Frozen alcohol makes as good a candle as wax, with one disadvantage: Alcohol melts at-114oC. What Fahrenheit temperature is this?

Temperature Ranges

Temperature Ranges

Thermal expansion

The Golden Gate Bridge has an over all length of ~2800m (mainly steel). If the bridge experiences temperature extremes from -20oC to +40oC, what will its change in length be?

Bimetalic strip

Nanomechanical Transducer

IBM laboratories,Rüschlikon, Switzerland500µm long100µm wide0.5µm thick

500µm

Peltier test for sensormechanical check

219 220 221 222 223 224 225 226 227 228 229

-200

0

200

400

600

800

1000

1200

1400

1600

heating test 30s, 0.75°C

de

f. n

m

min

Functionalized A

Functionalized B

Functionalized C

Fucntionalized D

Functionalized E

Functionalized F

Thermal Expansion Formulae

Sample Expansion ProblemFind the coefficient of expansion for a mysterious metal bar and use the table 5.1. to identify the metal. A bar with length 300 cm expands by 8.7mm when heated by 100 oC

Tll Δ⋅⋅=Δ αΔl is the change in lengthα is the coefficient of expansionΔT is the temperature change in oC

Coefficients of Linear Expansion at 2OoCSolids α (1/oC)Aluminum 25 x 10-6

Brass 19 x 10-6

Gold 14 x 10-6

Iron or steel 12 x 10-6

Lead 29 x 10-6

Silver 18 x 10-6

Glass (ordinary) 9 x 10-6

Glass (Pyrex) 3 x 10-6

Quartz 0.4 x 10-6

Concrete, brick 12 x 10-6

Marble (average) 2.5 x 10-6

LiquidsEther 550 x 10-6

Ethyl alcohol 370 x 10-6

Gasoline 320 x 10-6

Glycerin 170 x 10-6

Mercury 60 x 10-6

Water 70 x 10-6

GasesAir and most others 1100 x 10-6

at atmospheric pressure

Problem: linear expansion

?

copper

In the bimetallic strip shown the upper material is copper. Which of the following materials could be used for the lower metal? a) steel; b) brass; c) aluminum

Problem: linear expansion

The aluminum cone has been exactly fitted at 20oC to the copper block. Then it is taken out of the hole and at 180oC again placed inside. How much does the aluminum cone then stick out of the copper? (αCu=14.10-6 K-1, αAl=23.10-6 K-1

2o

3 cm

4 cm

Cu

Al

h2

h1

DensityIn physics, density is mass (m) per unit volume (V) — the ratio of the amount of matter in an object compared to its volume. A small, heavy object, such as a rock or a lump of lead, is denser than a larger object of the same mass, such as a piece of cork or foam

V

m=ρ

where, in SI Units:ρ (rho) is the density of the substance,measured in kg·m–3 m is the mass of thesubstance, measured in kg V is the volume ofthe substance, measured in m3

cgs units grams per cubic centimeter -> 1g/cm3=103kg/m3

Densities of various Substances(unless otherwise specified at 0oC and 1 atm)

SolidsAluminum 2.70Brass 8.44Copper' (average) 8.8Gold 19.3Iron or steel 7.8Lead 11.3Silver 10.1Uranium 18.7Concrete 2.3Cork 0.24Glass 2.6Granite 2.7Wood 0.3-0.9Ice (0oC) 0.917Bone 1.7

LiquidsWater (4oC) 1.000Blood, plasma 1.03Blood, whole 1.05Seawater 1.025Mercury 13.6Ethyl alcohol 0.79Gasoline 0.68Glycerin 1.26Olive oil 0.92

Gases (unless otherwise spec. at 0oC and 1 atm)

Air 1.29 x l0-3

Carbon dioxide 1.98 x 10-3

Carbon monoxide 1.25 x 10-3

Hydrogen 0.090 x l0-3

Helium 0.18 x 10-3

Methane 0.72 x 10-g

Nitrogen 1.25 x 10-3

Nitrous oxide 1.98 x 10-3

Oxygen 1.43 x l0-3

Water (100oC steam) 60 x l0-3

Heat capacity and latent Heat

Heat is defined as energy that flows as a result of temperature difference.

Heat capacity, Cp, of a body is defined as the quantity of heat absorbed or liberated, Q, by the body per unit temperature change, . The S.I. unit for heat capacity is J.K-1.

• s=Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval.

• Latent heat is defined as the quantity of heat absorbed or liberated by a substance in order to change a substance from one phase to another phase without a temperature change. The SI unit for latent heat is J.

• Specific latent heat of fusion of a substance, , is defined as the quantity of heat required per unit mass to change the substance from the solid phase to the liquid phase without a change in temperature.

• Specific latent heat of vaporization of a substance, , is defined as the quantity of heat required per unit mass to change a substance from the liquid phase to the vapour phase without a change in temperature.

TmsQ Δ⋅⋅=

Specific Heats of various substances at 20° C

Aluminum 0.217Brass 0.090Copper 0.092Gold 0.031Iron or steel 0.11Lead 0.030Silver 0.056Glass 0.20Ice (-5°C) 0.50Porcelain 0.26Wood 0.4Human Body (average) 0.83Protein 0.4

Ethyl Alcohol 0.58Glycerin 0.60Mercury 0.033Water (15°C) 1.000

Gases at Constant PressureAir 0.25Carbon Dioxide 0.199Helium 1.24Nitrogen 0.218Oxygen 0.218Water (100°C steam) 0.482

Substance s (cal/g.ºC, kcal/kg.ºC) Substance s (cal/g.ºC, kcal/kg.ºC)

Next Lecture

• To Be Covered: Phase changes and latent heat

• Reading: Chapter 5Section 5.3

Section 5.4